How to simplify?
(√3)/(√f^-3)
since √f = f^(1/2),
√(f^-3) = f^-(3*(1/2)) = f^(-3/2) = 1/(f√f)
so,
√3 / (1/f√f) = √3 * f√f = f√(3f)
How did you get the 1/(f√f)?
f^-1 = 1/f
f^-3 = 1/f^3
brush up on negative exponents, right?
They are evaluated as reciprocals.
Just an extension of the normal addition and subtraction of exponents.
since 1 = f^0,
f^-3 = f^(0-3) = f^0/f^3 = 1/f^3
To simplify the expression (√3)/(√f^-3), we need to simplify the numerator and the denominator individually and then combine the simplified terms.
Let's start by simplifying the numerator (√3).
The square root of 3 (√3) cannot be simplified any further since 3 is not a perfect square. Therefore, (√3) is the simplest form.
Now, let's simplify the denominator (√f^-3).
To simplify (√f^-3), we need to manipulate the exponent and rewrite it as a positive exponent.
Recall that the reciprocal of a number with a negative exponent is equal to the same number with a positive exponent. In this case, (√f^-3) can be rewritten as (√(1/f^3)), where we have inverted the fraction and changed the sign of the exponent.
Next, let's rationalize the denominator by multiplying the numerator and denominator by the conjugate of (√(1/f^3)), which is (√(1/f^3)).
(√f^-3) * (√(1/f^3)) = (√(f^-3 * 1/f^3))
Since we are multiplying similar terms, we can simplify the expression inside the square root:
(√(f^-3 * 1/f^3)) = (√(1/f^6))
Now, the square root of 1 (√1) is equal to 1, and we can rewrite (√(1/f^6)) as 1/(√f^6) or simply 1/f^3.
So, (√3)/(√f^-3) simplifies to 1/f^3.